离散数学

Preface

1SetsandLogic

1.1Sets

1.2Propositions

1.3ConditionalPropositionsandLogicalEquivalence

1.4ArgumentsandRulesofInference

1.5Quantifiers

1.6NestedQuantifiers

Problem-SolvingCorner:Quantifiers

Notes

ChapterReview

ChapterSelf-Test

ComputerExercises

2Proofs

2.1MathematicalSystems,DirectProofs,andCounterexamples

2.2MoreMethodsofProof

Problem-SolvingCorner:ProvingSomePropertiesofRealNumbers

2.3ResolutionProofst

2.4MathematicalInduction

Problem-SolvingCorner:MathematicalInduction

2.5StrongFormofInductionandtheWell-OrderingProperty

Notes

ChapterReview

ChapterSelf-Test

ComputerExercises

3Functions,Sequences,andRelations

3.1Functions

Problem-SolvingCorner:Functions

3.2SequencesandStrings

3.3Relations

3.4EquivalenceRelations

Problem-SolvingCorner:EquivalenceRelations

3.5MatricesofRelations

3.6RelationalDatabasest

Notes

ChapterReview

ChapterSelf-Test

ComputerExercises

4Algorithms

4.1Introduction

4.2ExamplesofAlgorithms

4.3AnalysisofAlgorithms

Problem-SolvingCorner:DesignandAnalysisofanAlgorithm

4.4RecursiveAlgorithms

Notes

ChapterReview

ChapterSelf-Test

ComputerExercises

5IntroductiontoNumberTheory

5.1Divisors

5.2RepresentationsofIntegersandIntegerAlgorithms

5.3TheEuclideanAlgorithm

Problem-SolvingCorner:MakingPostage

5.4TheRSAPublic-KeyCryptosystem

Notes

ChapterReview

ChapterSelf-Test

ComputerExercises

6CountingMethodsandthePigeonholePrinciple

6.1BasicPrinciples265

Problem-SolvingCorner:Counting

……

7RecurenceRelations

8GraphTheory

9Trees

10NetworkModels

11BooleanAlgebrasandCombinatorialCircuits

12Automata,Grammars,andlanguages

13ComputationalGeometry

AMatrices

BAlgebraReview

CPesudocode

References

HintsandSolutionstoSelectedExercises

Index

　　本书是“国外计算机科学教材系列”之一，全书共分13个章节，全面系统地介绍了离散数学的基础概念及相关知识，并在其前一版的基础上进行了修改与扩展。另外，书中还为各章配有相当数量的习题与书后的提示和答案，为读者迅速掌握相关知识提供了有效的帮助。可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。　　本书从算法分析和问题求解的角度，全面系统地介绍了离散数学的基础概念及相关知识，并在其前一版的基础上进行了修改与扩展。书中通过大量实例，深入浅出地讲解了数理逻辑、组合算法、图论、布尔代数、网络模型、形式语言与自动机理论等与计算机科学密切相关的前沿课题，既着重于各部分内容之间的紧密联系，又深入探讨了相关的概念、理论、算法和实际应用。本书内容叙述严谨、推演详尽，各章配有相当数量的习题与书后的提示和答案，为读者迅速掌握相关知识提供了有效的帮助。　　本书既可作为计算机科学及计算数学等专业的本科生和研究生教材，也可作为工程技术人员和相关人员的参考书。